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Questions tagged [abstract-algebra]

Abstract algebra is the study of algebraic objects. Some of the more common algebraic objects are groups, rings, fields, vector spaces, and modules, among other topics. Whenever you use this tag, please also include related tags like group-theory, ring-theory, modules, etc., in order to clarify which topic of abstract algebra is most related to your question and also to help other users find similar questions through the search engine.

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If $K/F$ is normal then $K/I$ is Galois.

Let $K/F$ be a normal extension and $I$ be the inseparable closure of $F$ in $K.$ Let $G=\text{Aut}_F(K),$ i.e., $F$ isomorphisms on $K$and similarly define $H=\text{Aut}_I(K).$ Now I have already ...